Concurrence depends on relative orientation of the polarization filters as well as on the detector positions!

b. Projection on measurementb. Projection on measurement

Setup for two atoms

John von Neumann(1903-1957)

Detectors in the far-fieldregion of the atoms

Detection projects system into a state compatible with the measurement result

Detection operatorfor detector j

laser pulse exciting both atoms

State after detection of two photons

Loss of which­way information introduces entanglementc. c. A multiple­emitter settingA multiple­emitter setting

Intensity-intensity distribution

Concurrence generated between the atoms

Abstract:Abstract:Incoherent scattering of photons off atoms can be described by a common Incoherent scattering of photons off atoms can be described by a common state of the atoms and the electric field [1,2]. A well-defined measurement state of the atoms and the electric field [1,2]. A well-defined measurement on the electric field thus projects the atoms into a certain final state [3-5]. on the electric field thus projects the atoms into a certain final state [3-5]. Here, we present a method how to use this technique to entangle remote Here, we present a method how to use this technique to entangle remote atoms to an arbitrary degree [6].atoms to an arbitrary degree [6].

References:References:[1] B.B. Blinov et al., Nature 428, 153 (2004). [5] Moehring et al., Nature 449, 68 (2007).[2] J. Volz et al., Phys. Rev. Lett. 96, 030404 (2006). [6] U. Schilling et al., Phys. Rev. A 80, 022312 (2009).[3] S. Bose et al., Phys. Rev. Lett. 83, 5158 (1999). [7] C. Thiel et al., Phys. Rev. Lett. 99, 193602 (2007).[4] C. Cabrillo et al., Phys. Rev. A 59, 1025 (1999). [8] T. Bastin et al., Phys. Rev. Lett. 102, 053601 (2009).

e. Generating arbitrary heralded entanglemente. Generating arbitrary heralded entanglement

Heralded entanglement of arbitrary degree in Heralded entanglement of arbitrary degree in remote atoms by detection of emitted photonsremote atoms by detection of emitted photons

Uwe Schilling*Uwe Schilling*11, Christoph Thiel, Christoph Thiel11, Enrique Solano, Enrique Solano22, Thierry Bastin, Thierry Bastin33, Joachim von Zanthier, Joachim von Zanthier11

11Institut für Optik, Information and Photonic, Universität Erlangen­Nürnberg, Erlangen, GermanyInstitut für Optik, Information and Photonic, Universität Erlangen­Nürnberg, Erlangen, Germany22Departamento de Química Física, Universidad del País Vasco – Euskal Herriko Unibertsitatea, Bilbao, SpainDepartamento de Química Física, Universidad del País Vasco – Euskal Herriko Unibertsitatea, Bilbao, Spain

22Institut de Physique Nucléaire, Atomique et de Spectroscopie, Université de Liège au Sart Tilman, Liège, BelgiumInstitut de Physique Nucléaire, Atomique et de Spectroscopie, Université de Liège au Sart Tilman, Liège, Belgium

*Email: uwe.schilling@physik.uni­erlangen.de*Email: uwe.schilling@physik.uni­erlangen.de

a. a. Spontaneous emission in a  ­systemΛSpontaneous emission in a  ­systemΛ

f. Estimates on the experimental feasibilityf. Estimates on the experimental feasibilityExpected count rate and generated concurrence

“Heralded entanglement of arbitrary degree in remote qubits”,U. Schilling, C. Thiel, E. Solano, T. Bastin, and J. von Zanthier,

Physical Review A 80, 022312 (2009)

Optical phase, accumulated by photon from atom n to detector j

Concurrence of

An entangled state of light and matter [1,2]

State of the system

Time dependent!

Polarizationfilter

Detection operator

Long-lived ground states(e.g. Zeeman states)

N trapped Λ-level atoms

N detectors in the far field

Initial state of the atoms

Detector extension:High count rate vs. high fidelity

Detection of first photon (generates W state)

Detection of N photons

Suitable choice of detector positions and polarizer orientations allows for a multitudeof long-lived states, e.g. all symmetric Dicke states [7], W -, and GHZ-states [8].

Concurrence

eigenvalues of

with

Pure states

with

Fix δ to odd multiple of π and use linear polarizers

“Malus law for the concurrence”

Realistic parameters:Distance between atoms 5 μm

Confinement of atoms 10 nm

horizontal angle α 5 mrad

Azimuthal angle φ Π/6 rad

Wavelength 650 nm

Repetition rate 5 MHz

Dark count rate ~200 Hz

Detector efficiency 30 %

Expected count rate: 1-10 Hz

Finite confinementof the atoms

Degradation of concurrence

Asymptotic final state,entangled!

No excitation left in the system → no decay

State of the atom after detection of a photon behind polarizer

N polarizers

α

φ